Suarez returned on Wednesday in the 1-0 Capital One Cup defeat at Manchester United from a 10-game suspension for biting Chelsea defender Branislav Ivanovic, having previously served an eight-game ban for clashing with Patrice Evra.
Ayre told Sky Sports News: "For all his controversy on the pitch, off the pitch he's a great guy, he's a family man and he's very well liked.
"He keeps himself to himself with his family, he's been committed he's worked hard, trained hard.
"It's been difficult, and been difficult for him really. It's always difficult being a footballer, and being a footballer like Luis Suarez you want to be on a football pitch.
"I think it's been a challenge for him but he's got through it and I think, and he's demonstrated last night, for a first game back, for somebody who hasn't had the opportunity to play in the Premier League this season, he acquitted himself very well."
Suarez signed an improved long-term contract with Liverpool in August 2012 and Ayre confirmed that the two parties would open talks over a new deal at the end of the current campaign.
Ayre said: "We sort of begin those type of discussions two years in from the end, so it'll be the end of this season. We'll do the same with everyone and at the right time we'll have the discussion with Luis and his advisors."
The Anfield supremo admitted Suarez's latest ban had hurt the global image of the club but that he and the player were keen to draw a line under it.
"Of course, any types of incident of that nature are damaging to a brand, but Liverpool Football Club is way, way bigger and always will be way bigger than any one player or one individual," Ayre added.
"Luis is a street fighter and we had to deal with it. We've worked a lot with him since the Ivanovic incident and he's back to what he's best at - terrorising defenders.
"We all move on together. Hard work and lessons have been learnt post-Evra and we now have a process in place for any crisis. Not a Suarez crisis, just any one."
Ayre also insisted he bore no ill will to Arsenal for trying to take Suarez to north London in a £40m and one pound transfer in the summer.
He said: "That's the transfer market. I have huge respect for Arsenal, they're a great football club, with some great people. I'm good friends with Ivan (Gazidis). Trying to get players, making offers for players, it's all part of the game.
"Anyone who says it isn't and makes a big noise is not really being honest. Everybody does the same thing in football, everybody's trying to achieve the same thing, we're all trying our best to buy the best players for the best price."
Ayre also gave Liverpool supporters some further encouragement when he described plans over the redevelopment of Anfield as having made "huge strides".
He added: "Our ambition is to stay at Anfield, and we're about 90% down the road in securing proprieties affected by redevelopment. I'm reasonably confident, the first phase will be closer to 60,000 capacity."
And he was also pleased with the way he and owners Fenway Sports Group were managing the club's operating debt and insisted that the cost of Anfield's redevelopment had also been considered.
He said: "You should always be worried but it is important we manage the debt. The business is headed in a positive direction and we will announce numbers in January next year.
"The business is in excellent health and moving towards a profitable position. The stadium's redevelopment is easily manageable."